C++ named requirements: RandomNumberDistribution (since C++11)

A RandomNumberDistribution is a function object returning random numbers according to a probability density function p(x) or a discrete probability distribution P(x i ) .

Requirements

The type D satisfies RandomNumberDistribution if

• D satisfies CopyConstructible
• D satisfies CopyAssignable

Given

• T , the type named by D :: result_type
• P , the type named by D :: param_type , which

• satisfies CopyConstructible
• satisfies CopyAssignable
• satisfies EqualityComparable
• has a constructor taking identical arguments as each of the constructors of D that take arguments corresponding to the distribution parameters.
• has a member function with the identical name, type, and semantics, as every member function of D that returns a parameter of the distribution
• declares a member typedef using distribution_type = D ;

• d , a value of type D
• x and y , (possibly const) values of type D
• p , a (possibly const) value of type P
• g , g1 , g2 , lvalues of a type satisfying UniformRandomBitGenerator
• os , lvalue of a specialization of std::basic_ostream
• is , lvalue of a specialization of std::basic_istream

The following expressions must be valid and have their specified effects

Expression	Type	Notes	Complexity
D::result_type	T	An arithmetic type	Compile-time
D::param_type	P		Compile-time
D()		Creates a distribution indistinguishable from any other default-constructed D	Constant
D(p)		Creates a distribution indistinguishable from D constructed directly from the values used to construct p	Same as p 's construction
d.reset()	void	Resets the internal state of the distribution. The next call to operator() on d will not depend on values produced by any engine prior to reset()	Constant
x.param()	P	Returns p such that D ( p ) . param ( ) == p	No worse than D(p)
d.param(p)	void	Postcondition: d. param ( ) == p	No worse than D(p)
d(g)	T	The sequence of numbers returned by successive invocations of this call with the same g are randomly distributed according to the distribution parametrized by d.param()	Amortized constant number of invocations of g
d(g,p)	T	The sequence of numbers returned by successive invocations of this call with the same g are randomly distributed according to the distribution parametrized by p	Amortized constant number of invocations of g
x.min()	T	The greatest lower bound on the values potentially returned by x ’s operator() , as determined by the current values of x ’s parameters	Constant
x.max()	T	The least upper bound on the values potentially returned by x ’s operator() , as determined by the current values of x ’s parameters	Constant
x == y	bool	Establishes an equivalence relation. Returns true if x. param ( ) == y. param ( ) and future infinite sequences of values that would be generated by repeated invocations of x ( g1 ) and y ( g2 ) would be equal as long as g1 == g2	Constant
x != y	bool	!(x == y)	Constant
os << x	Reference to the type of os	Writes a textual representation of the distribution parameters and internal state to os . The formatting flags and fill character of os are unchanged
is >> d	Reference to the type of is	Restores the distribution parameters and internal state with data read from is . The formatting flags of is are unchanged. The data must have been written using a stream with the same locale, CharT and Traits stream template parameters, otherwise the behavior is undefined. If bad input is encountered, is. setstate ( std :: ios :: failbit ) is called, which may throw std::ios_base::failure . d is unchanged in that case

Notes

The parameters of a distribution object may be changed either permanently, by using d. param ( p ) or just for the duration of a single operator() call, by using d ( g,p ) .

Calls to const member functions of the distribution and os << d do not affect the sequence of numbers produced by repeated d ( g ) .

Standard library

The following standard library components satisfy RandomNumberDistribution

uniform_int_distribution (C++11)	produces integer values evenly distributed across a range (class template)
uniform_real_distribution (C++11)	produces real values evenly distributed across a range (class template)
bernoulli_distribution (C++11)	produces bool values on a Bernoulli distribution (class)
binomial_distribution (C++11)	produces integer values on a binomial distribution (class template)
negative_binomial_distribution (C++11)	produces integer values on a negative binomial distribution (class template)
geometric_distribution (C++11)	produces integer values on a geometric distribution (class template)
poisson_distribution (C++11)	produces integer values on a poisson distribution (class template)
exponential_distribution (C++11)	produces real values on an exponential distribution (class template)
gamma_distribution (C++11)	produces real values on a gamma distribution (class template)
weibull_distribution (C++11)	produces real values on a Weibull distribution (class template)
extreme_value_distribution (C++11)	produces real values on an extreme value distribution (class template)
normal_distribution (C++11)	produces real values on a standard normal (Gaussian) distribution (class template)
lognormal_distribution (C++11)	produces real values on a lognormal distribution (class template)
chi_squared_distribution (C++11)	produces real values on a chi-squared distribution (class template)
cauchy_distribution (C++11)	produces real values on a Cauchy distribution (class template)
fisher_f_distribution (C++11)	produces real values on a Fisher's F-distribution (class template)
student_t_distribution (C++11)	produces real values on a Student's t-distribution (class template)
discrete_distribution (C++11)	produces random integers on a discrete distribution (class template)
piecewise_constant_distribution (C++11)	produces real values distributed on constant subintervals (class template)
piecewise_linear_distribution (C++11)	produces real values distributed on defined subintervals (class template)